d975e4302e
This is part of #3983. Fine-grained equational lemmas are useful even for non-recursive functions, so this adds them. The new option `eqns.nonrecursive` can be set to `false` to have the old behavior. ### Breaking channge This is a breaking change: Previously, `rw [Option.map]` would rewrite `Option.map f o` to `match o with … `. Now this rewrite will fail because the equational lemmas require constructors here (like they do for, say, `List.map`). Remedies: * Split on `o` before rewriting. * Use `rw [Option.map.eq_def]`, which rewrites any (saturated) application of `Option.map` * Use `set_option eqns.nonrecursive false` when *defining* the function in question. ### Interaction with simp The `simp` tactic so far had a special provision for non-recursive functions so that `simp [f]` will try to use the equational lemmas, but will also unfold `f` else, so less breakage here (but maybe performance improvements with functions with many cases when applied to a constructor, as the simplifier will no longer unfold to a large `match`-statement and then collapse it right away). For projection functions and functions marked `[reducible]`, `simp [f]` won’t use the equational theorems, and will only use its internal unfolding machinery. ### Implementation notes It uses the same `mkEqnTypes` function as for recursive functions, so we are close to a consistency here. There is still the wrinkle that for recursive functions we don't split matches without an interesting recursive call inside. Unifying that is future work.
38 lines
748 B
Text
38 lines
748 B
Text
def Nat.isZero (x : Nat) : Bool :=
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match x with
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| 0 => true
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| _+1 => false
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axiom P : Bool → Prop
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axiom P_false : P false
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/--
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info: x : Nat
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⊢ P (1 + x).isZero
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-/
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#guard_msgs in
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example (x : Nat) : P (1 + id x.succ.pred).isZero := by
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dsimp
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trace_state
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simp [Nat.succ_add]
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dsimp [Nat.isZero]
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apply P_false
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp [Nat.isZero]
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apply P_false
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp [Nat.isZero.eq_2]
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apply P_false
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example (x : Nat) : P (id x.succ.succ).isZero := by
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dsimp!
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apply P_false
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@[simp] theorem isZero_succ (x : Nat) : (x + 1).isZero = false :=
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rfl
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theorem ex1 (x : Nat) : P (id x.succ.succ.pred).isZero := by
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dsimp
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apply P_false
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